Sensorless position control of Permanent Magnet Synchronous Machines without Limitation at Zero Speed

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1 Snsorlss posiion onrol of Prmann Magn Synhronous Mahins wihou Limiaion a Zro Spd Maro Link, Sudn Mmbr, Ralph Knnl, Snior Mmbr, Joahim Holz, Fllow Univrsiy of Wuppral Elrial mahins and drivs hp:// Absra Snsorlss posiion onrol of Surfa Mound Prmann Magn Synhronous Mahins (SMPMSM sill is a hallng. High prforman posiion onrol a low and zro spd is only possibl using anisoropi ffs bing no onsidrd in h fundamnal-frquny mahin modls bu in xndd highfrquny modls. This papr prsns a nw highfrquny injion mhod simaing h roor posiion, whih ovroms h small signal o nois raio inhrn o mhods of his yp publishd so far. This nabls o rak vn small salinis ypial for SMPM synhronous mahins. A small high-frquny volag signal is injd ino h roor d-axis wih no influn on h orqu produing q-urrn. Th dmodulaion of h rsponding high-frquny urrn signal is indpndn on mahin paramrs. Thrfor h proposd mhod is indpndn on mahin paramrs and simply adapabl o diffrn mahins. As only h high frquny urrn has o b prossd for posiion simaion, hr is no addiional hardwar nssary bsids ha for sandard drivs wih fild orind onrol. Indx rms snsorlss posiion onrol, highfrquny injion, anisoropi mahin propris, signal modulaion, surfa mound prmann magn synhronous mahin I. INTRODUCTION Snsorlss onrol shms basd on fundamnalfrquny mahin modls fulfill dmands in highr spd rangs. Posiion onrol as wll as appliaions rquiring prmann opraion a low spds anno b obaind by hs mhods. This is owd o a loss of informaion on h roor sa whn h indud roor volag boms vry small as h roor spd rdus. Th ff is no limid o a pariular yp of rvolving fild mahins; i is assoiad wih asynhronous mahins as wll as wih synhronous mahins. An addiional problm is h obsrvr sruur mosly usd in fundamnal simaion mhods dpnding srongly on mahin paramrs. Pariularly wih asynhronous mahins vn small simaion rrors in mahin paramrs add offss of abou half h slip dpnding on h auray of mahin paramr simaion. Posiion simaion is gnrally impossibl du o h salar spd simaion whn using fundamnal sa obsrvrs. Thorially h posiion an b alulad by ingraing h spd, bu in prai h rsul will suffr undr drif problms. An inrsing fild of rsarh rlas o high prforman snsorlss posiion onrol of synhronous mahins, whih an b onsidrd as mor sringn rquirmn han jus mainaining zro spd [1, 11]. I involvs zro spd opraion a a prdrmind roor posiion. Papr publishd rnly india high-frquny injion mhods boming mor and mor araiv [1, 4, 5]. Th absn of posiion snsors rquir h onrol algorihm o rfr o anisoropi propris in salin a-mahins. Salinis ar no rsrid o a spifi mahin yp. Thy ar wll known in Synhronous Rluan Mahins as wll as in Inrior Prmann Magn Mahins, bu hy also xis - vn if no dominaing - in induion mahins (roor slos and Surfa Mound Prmann Magn Synhronous Mahins. Mos mhods publishd so far fail o rak rliably small anisoropis in hs yps of AC mahins. Thy suffr mainly undr a small signal-o-nois raio and a low spaial rsoluion. To xpand h appliaion ara of high-frquny mhods hr is an inrasing ffor o dsign arifiial salinis in mahins wih originally small salinis [2]. Mos publishd mhods whih ar abl o rak vn small salinis nd addiional volag snsors [1, 12] and rquir high rsoluion dion of zro rossings of high frquny urrns, whih ar diffiul o d in noisy nvironmn [11] or rquir dir ass o mahin rminals for zro volag dion [12]. Small salinis inras h problm of pris volag injion aording o rvolving high frquny signals - h nonlinar bhavior of h invrr onsidrably drass h simaion sabiliy and posiion auray [9]. Th mhod proposd in his papr prsns som progrss in ovroming h problms addrssd abov by using a nw xiaion mhod basd on a high frquny ampliud modulaion mhod. Th mhod rquirs no addiional hardwar or snsors, and is insnsiiv o paramr variaions as wll as o addiional parasii salinis ha ar no onsidrd in h modl.

2 II. HIGH-FREQUENCY INJECTION High-frquny injion mhods gnrally offr h possibiliy o obsrv h mahin spd and/or posiion indpndn on h fundamnal supply volag and urrns. Signal injion mhods ar suid o xploi mahin propris ha ar nihr onsidrd in h fundamnal mahin sa variabls nor in h fundamnal mahin modl. Th high-frquny flux mainly propagas hrough h lakag pahs in h saor and roor. Du o h skin ff, howvr, h oupling of h high-frquny flux wih h roor is rahr small and i is limid o rgions los o h surfa. Som signal injion shms us only urrn snsors, whih ar anyway nssary for fild orind onrol [2, 3]. Using h volag injion prinipl insad of h urrn injion shms, volag snsors an b omplly avoidd. Thr ar no rquirmns for addiional hardwar and for synhronizaion wih h PWM puls parn as nssary in ohr mhods [1, 12]. Th absn of volag snsors onsius a major bnfi of highfrquny injion mhods. In high-frquny mhods, h physial ff usd for posiion dion bass on mahin anisoropis. A high-frquny signal gs modulad by h salinis of h lrial mahin. To d ha ff, i is possibl o inj a volag and monior h urrn or o inj a urrn and o monior h volag. Du o h limid bandwidh of h urrn onrol loop i is prfrrd o inj a volag, as i is don in h mhod proposd in his papr. II. A. Rprsnaion of anisoropis in synhronous mahins Anisoropi mahin bhaviour rsuls in diffrn induans wih rsp o a dq-rfrn fram ha is synhronizd wih h roor anisoropis. Th flux indud by h high arrir frquny is mainly onnrad on h flux linkag hrough h lakag induan: (A l σ = (2.1 l Th induan nsor l σ (A rprsns high frquny lakag induans in h rfrn fram alignd wih h anisoropy. (markd wih indx (A A singl dominan anisoropy, ausd by h main flux, hararizd by a singl spaial yl pr pol pih, is ypial for SMPMSMs. This fa jusifis h simplifiaion o align h anisoropy wih a fild orind dq-rfrn fram. (A (F l σ = l σ (2.2 II. B. Th basi sruur of rvolving high-frquny signal injion Th lassial injd rvolving volag, ras a oninus high frquny sinusoidal urrn usually alld arrir urrn. A roaing arrir signal aording o [2, 1] an b rad as jω u = u (2.3 onsidring ω as arrir frquny. Th indx rfrs o h saor oordina sysm and u is h volag ampliud Fig.1: A basi sruur of snsorlss driv shm using sinusoidal highfrquny injion wih rvolving arrir signal [2] of h arrir signal suprimposd o h fundamnal volag. Th modulaion of h injd high frquny signal by h mahin anisoropis rsuls in urrns ha ar rprsnd by h spa vor i. Th high frquny omponns an b alulad by h diffrnial saor quaion in synhronous oordinas for high frqunis. (A d (A (A i j( ω ω u a σ = u = l (2.4 d Consqunly h volag vor is modifid by h angular vloiy ω a of h saliny. Th rsuling high frquny urrn an b dsribd as j( ω ωa u ( l + (A i = j.(2.5 j( ω ω 2(ω l l ωa a + ( l

3 As h arrir frquny ω is hosn o b subsanially highr han ω a, h urrn an b dsribd by (2.6, following a r-ransformaion o saionary oordinas. This lads o (F j( ˆ u = u os ( ω. (3.3 i u = j 2ω l = i + i p n l ( l + ( l + l l jω j(ω 2ωa (2.6 In his quaion, h posiiv urrn squn omponn i p, roas a posiiv arrir frquny; i onains no informaion on h roor posiion. Th ngaiv urrn squn omponn i n roas a an angular vloiy -ω + 2ω a and onains h dsird informaion onrning h angl ω a of h anisoropy. Th high frquny urrn omponn is sparad by a bandpass filr from h fundamnal frquny omponns and from h wid sprad invrr frquny sprum. Fig. 1 illusras h basi prinipl. Th low pass filr liminas h high-frquny urrn from h fundamnal urrn insid h urrn onrol loop. An obsrvr for h high frquny urrn prosss h anisoropy modl and provids roor spd and posiion simaion. i = III. PROPOSED AMPLITUDE MODULATED SPACE VECTOR METHOD Th diffrnial quaion (3.4 is similar o (2.4. (F (F j( ˆ (F d i u = u os ( ω = lσ (3.4 d Saor rsisan, indud volag and ross oupling of h urrns ar ngld in h diffrnial saor quaion similar o (2.5. This is only prmid if h arrir frquny ω is muh highr han h fundamnal frquny. Th ral fild angl is h unknown variabl in his quaion. Th soluion in fild oordinas of (3.4 is (F u 1 1 i = sin ω os( + j sin(. (3.5 ω l Th ransformaion o saionary oordinas rsuls in j(ω + j(ω + ˆ 2 ( l d ( d σ + l lσ l + 1 j4 ω l d q j( ω ˆ j( ω ˆ 2 σ lσ ( l d + + ( d σ l lσ l = ip + in u (3.6 III. A. Drivaion of h arrir signal Th arrir injion mhods publishd so far suffr from som drawbaks. Th poor signal-o-nois raio and h paramr dpndn of h obsrvr o pross h high frquny urrn rdu h snsiiviy of h onp for small salinis. Th nw mhod gnras a posiiv as wll as a ngaiv urrn squn omponn, boh onaining informaion abou h roor posiion. Th injd arrir volag j a u = u os ( ω (3.1 is always in alignmn wih h simad posiion of h anisoropy (simad valus ar markd wih a ha ^: ˆ = ωˆ a. (3.2 a Th anisoropy in a SMPMSM is mainly basd on h sauraion ff of h main flux; i roas a h sam frquny ω as h roor. Th subsrip a gnrally indias an anisoropy-alignd oordina sysm as opposd o h fild orind sysm. Boh oinid in h as of surfa mound PMSM. A ransformaion of h arrir volag o fild oordinas is don by muliplying (2.3 by -j. Th analysis of h spral omponns of h saor urrn provids som inrsing rsuls. III. B. Analysis of h high-frquny urrn Th saor urrn dsribd by (3.6 an b sparad in a posiiv squn omponn i p and a ngaiv squn omponn. Ohr han h urrn in (2.6, also h posiiv squn omponn onains informaion abou h fild posiion angl. Th informaion onn of h frquny sprum inrass. Figur 2 illusras h frquny sprum of h urrns (3.6. Th ngaiv and posiiv frquny rang onain j(- ω -+2 ^ ngaiv squn j(- ω + ^ i K( l l + l ω - l ω ω ω Fig. 2: Complx frquny sprum of h high frquny urrn i aording o 3.6 for small salinis posiiv squn j( ω -+2 ^ j( ω + ^

4 fild angl informaion, h ampliud of whih is proporional o h diffrn of d- and q-lakag induans. Th formr inuiiv assumpion of small anisoropis (l - l bing dirly rlad o a low-ampliud informaion onn in h posiiv and ngaiv squn omponns is hrby onfirmd (Fig. 2 I is vidn from (3.5 ha h imaginary par of h high frquny urrn drass whn h simad angl approahs h ral fild angl and finally boms zro. Hn h harmoni orqu disorion du o h s signal is ngligibl. IV. DEMODULATION OF THE CARRIER SIGNAL Using high frquny injion mhods for snsorlss onrol, h signal dmodulaion onsius a major dmand for signal prossing. To rdu h alulaion, h highfrquny urrn i (3.6 is ransfrrd o a rfrn fram in a ngaiv dirion a approxima arrir frquny. This is don by ( ω+ -j( ω+ i = i (4.1 This ransformaion gnras a high frquny urrn signal ha is asy o dmodula wihou rfrring o mahin paramrs. Assuming h rmaining ngaiv squn urrn omponns of i is rjd by a low pass filr, ransformaion (4.1 applid o h urrn signals (3.6 rsuls in ( + l ( ω + 1 i = p u ω j(2-2 j4 l. (4.2 ( l h arrir volag o h simad anisoropy angl is possibl and provd by quaion (4.2. To inras h ovrall snsiiviy of h snsorlss onp, h sam dmodulaion mhod as dsribd abov for h posiiv urrn omponn of quaion (2.6 an b applid o h ngaiv urrn squn omponn. (-ω+ j( ω i = i (4.5 Th rsul is similar o (4.4 wih h diffrn ha h ngaiv frquny rang b xploid for raking h fild angl. Using boh signals (4.1 and (4.5 drass h possibl rrors and olrans whn prossing h roor posiion. V. SENSORLESS POSITION CONTROL OF SMPMSM As disussd in Chapr IV, a omplx dmodulaion of h arrir an b rplad by raking h rror simaion signal (4.3. Th horial valuaion onfirms ha i is possibl o gnra a alulaion quaniy rprsning h misalignmn bwn h simad fild angl and is ru valu, (4.4. Traking an rror signal is robus agains nois and masurmn olrans.g. h limid rsoluion of h analog o digial onvrr in driv onrollrs. As h simad fild rror angl is valuad in h proposd mhod insad of fild angl islf, h rsoluion of h high frquny urrn signal i is lss riial. Th rror signal is as an inrmnal variabl ha hangs only slowly in omparison o h sampl frquny. I an asily b sparad baus i is ransformd by (4.1 o abou wi h arrir frquny. Equaion 4.2 illusras h urrn rspons onaining h usful informaion abou h misalignmn of h simad fild angl wih rfrn o h ral fild angl. I an b rgardd as an rror simaion angl =. (4.3 Th urrn rspons is furhr simplifid o rdu prossing powr nssary for dmodulaion. In h as of small rror simaion angls h urrn rspons is: - j( σ + ( ω + 1 l d l i p = u (4.4 4 ω l ( l 2 This quaion shows h ral par of h urrn rspons in h rfrn fram aording o (4.1 bing proporional o h rror angl. This is usd o rak h fild angl by a losd loop raking sysm. Th basi prinipl of adjusing Fig.3: Signal flow graph of h fild angl simaion shm basd on h proposd mhod

5 Th signal flow graph in Figur 3 illusras h basi sruur of h proposd snsorlss shm. Th posiiv squn urrn in (4.4 has a ral omponn proporional o h rror angl. This signal is sampld a h sampling frquny of h urrn onrol loop. Th following PIonrollr fds a onrolld osillaor o ra h simad fild angl. This rsuls in a losd loop sruur ha orrs h fild angl in ah sampling yl. A high sampling frquny nsurs good and dynamially fas alignmn wih fild axis. Th disurbans of h aquird signal ar low, hus prmiing opraion a low arrir ampliuds. Th prominn advanag is ha h raking obsrvr dos no rquir any mahin paramrs. To sablish narrow filr hararisis, h urrn i in Fig. 3 is ransformd o h simad fild oordina sysm by ( -j( i = i. (5.1 This ransformaion rsuls only in urrn omponns of arrir frquny ω. This allows using narrow band filrs ha rj all frqunis xp h arrir frquny, whih is ssnial o sima small salinis 1. VI. EXPERIMENTAL RESULTS Th fild axis is fixd o h roor only a noload; hrfor h roor posiion an b hn drivd from h simad fild angl. Howvr, a small diffrn xiss bwn boh angls whn a load is applid. A linar ompnsaion rlad o h orqu urrn rdus his ff subsanially. Th simad roor fild angl is hrfor onsidrd in alignmn wih h roor posiion angl. Exprimnal rsuls wr obaind using a ommrial 6- pol SMPMSM srvo driv (s Tabl 1: Tabl 1: hnial daa SMPMSM Rad powr 1.2 kw Rad spd 6 rpm Rad volag 4 V Rad urrn/ max. urrn 2,8 A/ 15.2 A ms Fig.4: Sp rspons of h fild raking sysm, masurd roor posiion and simad roor angl afr ford rs o zro Th swihing frquny is 8 khz, h arrir frquny is 2 khz wih a pak arrir urrn i,.max of 2 ma. Th urrn is prossd by h sam sandard 12-Bi A/D onvrr usd for snsing h fundamnal urrns. Th saliny raio in his mahin is small, rfld in a lakag induan raio of:. 9 l (6.1 In omparison o ha, an isoropi mahin has an induan raio los o 1. Small salinis rquir a highly snsiiv simaion mhod, whih mus b robus agains parasii anisoropis lik invrr lamping ffs [9]. Th high arrir frquny nsurs a high dynami bandwidh of h simaion mhod, whih is nssary for srvo driv appliaions. Fig. 4 illusras h rspons of h fild raking onrol loop afr foring h simaion angl o zro. - /1 - -/ ms Fig.5: Masurd roor posiion and posiion rror bwn h masurd and simad posiion, simad posiion (half of rad load, sady sa opraion ωˆ ω R ωˆ For valuaing h auray of h snsorlss posiion idnifiaion mhod, sady-sa ss wr prformd. Th ms Fig.6: Rspons o ommandd sp hangs of on full rvoluion. Only h simad posiion and simad roor spd ar usd for driv onrol, whil h masurd posiion is only a rfrn

6 fild raking onrol is basd on a PLL sruur (Fig. 3. Thrfor i is fr of phas lags a sady-sa opraion. Th auray and rsoluion of h snsorlss posiion simaion mhod is illusrad in Fig. 5. Posiioning appliaions rquir rpaabl opraion o prdrmind angular roor posiions. Fas dynami posiion onrol is nssary o provid ha h mhod offrs rpaabl dynami posiioning opraion wihou snsing h posiion vn wih rad load (Fig.6. Th proposd high-frquny mhod is mainly appliabl o opraion a low fundamnal frqunis. Fig. 7 shows a posiioning s. During h opraion h driv opras a a fundamnal frquny of 6 Hz. This is possibl, baus h filr hararisi of h narrow band pass filr sparas h high frquny omponns from nois and h fundamnal frquny. ωˆ ωr.2 - i sq 2 i sr VII. CONCLUSION.4 s Fig.7: Snsorlss posiioning, simad posiion and simad roor spd ar usd for driv onrol, h urrn i sq is limid o wi h rad urrn i sr. This papr prsns a nw snsorlss onrol algorihm for Surfa Mound Prmann Magn Synhronous Mahins using high frquny volag injion. Th mhod is abl o rak vn small salinis in lrial mahins. Th injion of ampliud modulad arrir signals, as an ovrlay o h fundamnal frquny, offrs a highly snsiiv saliny dion mhod. Wih rsp o anisoropis ausd by sauraions, h maximum flux dnsiy ours in dirion of h d-axis of a fild orind oordina sysm and an b rgardd as fixd o h roor. Thrfor h simaion of roor posiion basially rsuls in ding h flux angl and modling h phas shif bwn hm. Considring his, h mhod is indpndn of mahin paramrs as only a posiion rror is simad and rakd by los loop obsrvr. Th xprimnal rsuls vrify his mhod o d rliably vn small salinis in SMPMSM and xploi hm for high dynami posiion onrol. Th mhod provids main advanags a low and zro spd. REFERENCES [1] J. Holz, Snsorlss Posiion Conrol of Induion Moors - an Emrging Thnology, IEEE Transaions on Indusrial Elronis, Vol. 45, No. 6, Dmbr [2] Robr D. Lornz, Snsorlss Driv Conrol Mhods for Sabl, High Prforman, Zro Spd Opraion, Inrnaional Confrn on Powr Elronis and Moion Conrol- EPE-PEMC, Kosi 2. [3] J.K Ha, S.K. Sul, K. Id, I. Murokia, K. Sawamura, Physial Undrsanding of High Frquny Injion Mhod o Snsorlss Drivs of an Induion Mahin, IEEE-IAS 2, Confrn Rord of h 2 IEEE Ind. Appl. Confrn, Vol.4 [4] J.K. Ha, S.K. Sul, Snsorlss Fild-Orinaion Conrol of an Induion Mahin by High-Frquny Signal Injion, IEEE Tran. On Ind. Appl., Vol. 35. No.1, Jan./Fb [5] A.Consoli, F. Russo, A. Tsa, Low- and Zro-Spd Snsorlss Conrol of Synhronus Rluan Moors, IEEE Trans. On Ind. Appl., Vol.35, No.5, Sp./O. 1999,pp [6] J. Holz, Th Dynami Rprsnaion of AC Driv Sysms by Complx Signal Flow Graphs, Conf. Rord of ISIE (Inrnaional Symposium on Indusrial Elronis, Saniago d Chil, Chil, 1994, pp. 1-6 [7] M.Shrodl, Snsorlss onrol of AC Mahins a Low Spd and Sandsill basd on h INFORM Mhod, IEEE Ind. Appl. Soiy Annual Ming, Pisburgh, Sp.3- O. 4, 1996, pp [8] N. Tsk, G. M. Ashr, M. Sumnr, K.J. Bradly, Supprssion of Sauraion Saliny Effs for h Snorlss Posiion Conrol of Induion Moor Drivs undr loadd Condiions, IEEE Trans. on Ind. El., Vol. 47, No. 5, Sp/O. 2, pp [9] N. Tsk, G.M Ashr, K.J. Bradly, M.Sumnr, Analysis and Supprssion of Invrr Clamping Saliny in Snsorlss Posiion Conrolld Induion Moor Drivs, IEEE Ind. Appl. Soiy Annual M., Chiago, Sp. 3 O. 4, 21 [1] F. Briz, M.W. Dgnr, A. Diz, R.D. Lornz, Sai and Dynami Bhaviour of Sauraion-Indud Salinis and hri Eff on Carrir Signal Basd Snsorlss AC Drivs, IEEE Ind. Appl. Soiy Annual M., Chiago, Sp. 3 O. 4, 21 [11] A. Consoli, G. Sarlla, A. Tsa, Indusry Appliaion of Zro-Spd Snsorlss Conrol Thniqus for PM Synhronous Moors, IEEE Trans. on Ind. Appl., Vol. 37, No.2, Marh/April 21 [12] A. Consoli, G. Sarlla, A. Tsa, A Nw Zro Frquny Flux Dion Approah for Dir Fild Orind Conrol Drivs, IEEE Trans. on Ind. Appl., Vol. 36, No.3, May/Jun 2, pp